Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is
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a
5
b
8
c
6
d
10
answer is D.
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Detailed Solution
Frequency in a stretched string is given by n=12lTπr2ρ=1lTπd2ρ (d = Diameter of string)⇒n1n2=l2l1T1T2×d2d12×ρ2ρ1 =353681×142×21=3536⇒n2=3635×360=370Hence beat frequency = n2−n1=10
Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is